Title: Covolumes of arithmetic subgroups of simple real Lie groups

Abstract: Lattices in Lie groups, i.e. discrete subgroups of finite covolume play an important role in geometry and arithmetic. If G denotes a simple Lie group then of particular interest is the set of covolumes vol(G/L), where L runs over all lattices in G. For instance, one can ask if this set has a minimum and how often this minimum is attained. The intention of my talk is to report on some well-known results and also on a recent work on lattices of minimal covolume in Lie groups, which is a joint work with K. Holm and R. Köhl.